More precisely, the invention concerns a mechanical system capable of providing restoring forces characterized by non-linear hysteresis loops, whose shapes can be adjusted depending on the specifications required by the application. The forces are to be carried for example by wire ropes composed of steel and shape-memory material wires. The system is represented by a closed frame within which groups of wire ropes are housed, connected on one side to two parallel uprights and on the other side to a pair of rigid metal elements subject to equal displacement for the presence of two smooth bars crossing them and on which they can slide substantially without friction. Such smooth bars are fixed in the center line to a further central metallic element with respect to the other, which in turn can slide without friction on two additional smooth bars orthogonal to the previous ones and which act as guide shafts. The latter are fixed to the ends to two parallel sides of the closed frame. The set of the three elements and of the two smooth bars crossing them constitutes the secondary frame whose translation relative to the closed frame in the direction orthogonal to the ropes produces the nonlinear hysteretic restoring forces. When the secondary frame acts as vibrating mass, being capable of sliding on the underlying guides, the device operates as a vibrations damper. When the above system is introduced into a metal rod, the rod becomes a dissipative damping brace thanks to the dissipation exerted by the mechanism. When the device is configured in such a way that the sliding central element supports a structure while the closed frame is fixed to a base subject to undesirable motions (e.g. seismic motion or motion induced by machinery), the body acts as a vibrations hysteretic isolator for the main structure. When the closed frame is fixed on a movable member and the secondary frame impacts on an obstacle, the device exerts its action by absorbing shocks.